480 x - STATICS OF DEFORMABLE BODIES. 



From the first of a) and b), by differentiation, 



74) l** v gfj ^ 0** 



From a), 



n ~\ Bu , Bv , dw ,+ 



The equations 73) become 



c) ; ^ 



B*w 



3*W . ^ V <AJ ~ 



= U. 



The equations a), b), c), d), e), together with the surface condi- 

 tion at the cylindrical surface 



75 r JT~J cos ( n y) ^ u> 



and the conditions 71) at the origin, constitute the mathematical 

 statement of the problem. 



Differentiating e) by #, and subtracting the derivative of c) by x 

 and of d) by y, 



77) 



Inserting the values of -- and ^- in terms of -- from a) gives 



78) |^ = 0. 



Adding the derivative of c) by y and of d) by x, 



79) 



<?2/ o 

 which, by use of b), gives 



80) dxdydz = a 



Differentiating e) by 0, and using 78), 



= 0. 



Differentiating c) by x, d) by y, and comparing with a), 

 82) 



